Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

For nearly 70 years, the solution to the discrete ordinates approximation of the ID monoenergetic neutron transport equation has been an effective approximation. During that time, the method has experienced numerous improvements as numerical and computational techniques have advanced. Here, we propose a new, consistent expression of the analytical solution to the ID, monoenergetic discrete ordinates (DOM) equations, called the Response Matrix DOM (RM/DOM), which is an improvement over past forms. The approach takes advantage of the second order form of the discrete ordinates approximation to express the solution as hyperbolic functions rather than ordinary exponentials. By comparison, a highly anisotropic radiative transfer benchmark will demonstrate the precision of the solution. We then establish a new high order benchmark for scattering in a purely hydrogenous medium and apply RM/DOM to general monoenergetic elastic scattering.

Original languageEnglish (US)
Title of host publicationMathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015
PublisherAmerican Nuclear Society
Pages1327-1338
Number of pages12
Volume2
ISBN (Print)9781510808041
StatePublished - 2015
EventMathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 - Nashville, United States
Duration: Apr 19 2015Apr 23 2015

Other

OtherMathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015
CountryUnited States
CityNashville
Period4/19/154/23/15

Fingerprint

Discrete Ordinates
Neutron Transport
Transport Equation
neutrons
Approximation
matrices
approximation
Scattering
Benchmark
hyperbolic functions
Hyperbolic function
Radiative Transfer
Computational Techniques
Numerical Techniques
radiative transfer
Analytical Solution
elastic scattering
Express
Higher Order
scattering

Keywords

  • Anisotropic scattering
  • Convergence acceleration
  • Diagonalization
  • Second order ODE

ASJC Scopus subject areas

  • Mathematics(all)
  • Nuclear and High Energy Physics

Cite this

Ganapol, B. D. (2015). Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation. In Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 (Vol. 2, pp. 1327-1338). American Nuclear Society.

Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation. / Ganapol, Barry D.

Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015. Vol. 2 American Nuclear Society, 2015. p. 1327-1338.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ganapol, BD 2015, Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation. in Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015. vol. 2, American Nuclear Society, pp. 1327-1338, Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015, Nashville, United States, 4/19/15.
Ganapol BD. Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation. In Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015. Vol. 2. American Nuclear Society. 2015. p. 1327-1338
Ganapol, Barry D. / Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation. Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015. Vol. 2 American Nuclear Society, 2015. pp. 1327-1338
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